CN110378018A - A kind of calculation method of the stable state bearing capacity of liquid ball bearing - Google Patents
A kind of calculation method of the stable state bearing capacity of liquid ball bearing Download PDFInfo
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Abstract
The calculation method of the stable state bearing capacity of liquid ball bearing according to the present invention, comprising the following steps: 1, establish oil film pressure computation model；2, hydrodynamic lubrication oil film pressure computation model is established in the difference expression of spherical coordinate system；3, calculate the oil film thickness of bearing；4, initial pressure value is set, oil film pressure is calculated；5, by oil film pressure along lower three Directional Decompositions of rectangular coordinate system；6, oil film circumferencial direction and radial direction pressure are integrated, the bearing capacity in circumference x, y, z direction is respectively obtained；7, to bearing capacity formula nondimensionalization, obtain dimensionless bearing capacity；8, dimensionless Bearing Capacity Formula is integrated, the bearing capacity of bearing is obtained.Since the calculation method of the stable state bearing capacity of liquid ball bearing of the invention is based on three-dimensional shafting, therefore, the stable state bearing capacity result of obtained liquid ball bearing can preferably reflect truth, preferably can provide theoretical direction for the structure design of liquid ball bearing.
Description
Technical field
The invention belongs to machinery fields, and in particular to a kind of calculation method of the stable state bearing capacity of liquid ball bearing.
Background technique
Ultra precision machine tool and material are simultaneously known as " mother of industry ", and precision and ultra-precision machining technology and equipment is highly sophisticated products
With key technology one of of the national defense industry in the world is striven.Microscale-nanoscale ultraprecise equipment, chief is rotary part,
I.e. the machine tool headstock with ultraprecision spindles rotary axis system is just capable of measuring and processes ultraprecise part.Ultraprecision spindles require to reach
The high rigidity that arrives, high rotating accuracy, stability of rotation, without friction, key is precision bearing used.
Liquid ball bearing is the significant components of ultraprecise and heavy machine tool, it can not only bear axially and radially to carry simultaneously
Lotus, and it is convenient for centering.These bearings have high running accuracy, dynamic stiffness height, vibration damping height, performance with long service life excellent
Gesture.Liquid ball bearing can reduce bearing wear when conventional hybrid bearing low speed.
Spherical liquid bearing is made of rotor (convex ball) and stator (recessed ball) two parts, there is a certain number of oil on stator
Hole.On the one hand, the oil liquid that certain pressure is exported by oil pump flows into bearing clearance and forms static pressure oil film and shape by flow controller
At static pressure bearing capacity.On the other hand, wedge shape oil is formed by running at high speed between bearing surface, between rotor and stator,
It generates dynamic pressure oil film and forms dynamic pressure bearing capacity.
Shape liquid-bearing in the rotary course of supporting spindle due to the presence of gravity and rotary centrifugal force so that oil film is thick
Degree is unevenly distributed, therefore results in that oil film pressure distribution is uneven, and then has larger impact to the bearing capacity of bearing.It is setting
Meter needs to establish it suitable computation model before manufacturing.Scholar studies on academic journal and is concentrated mainly on gas at present
On ball bearing, and the compressibility of gas, so that gaseous sphere bearing rigidity is lower, bearing capacity is poor, at the same gas bearing and
There is biggish otherness on the layout strategy and technical solution that liquid-bearing is considered, so that liquid spheres bearing film carries energy
Power and the bearing capacity of gas ball bearing have a great difference.
Journal article " hemisphere face gas bearing stable state Analysis of Bearing Capacity " equally sampling is established gas lubrication Reynolds equation and is asked
Gas film pressure, establishing gas lubrication equation due to gas compressibility, gas density with pressure and temperature variation
And change, and the variation of the density approximation definite value of liquid, i.e. liquid density with temperature and pressure hardly changes, so liquid moistens
Sliding Reynolds equation and having differences property of gas lubrication Reynolds equation；When calculating ball bearing bearing capacity, liquid ball bearing is held
Loading capability is more much bigger than gaseous sphere bearing load carrying capacity, also has because of the difference of the threedimensional model of ball bearing in calculation method
Fine difference.Bearing radial direction bearing capacity is only discussed in above-mentioned paper, there is no calculate axial carrying capacity.
Summary of the invention
In order to solve the problems, such as that liquid spheres bearing film bearing capacity, the present invention pass through in the three-dimensional geometry mould for establishing ball bearing
It type and establishes on ball bearing hydrodynamic lubrication Reynolds equation basis, under given certain pressure and the speed of mainshaft, calculates
Three, liquid ball bearing direction bearing capacitys.
The present invention provides a kind of calculation methods of the stable state bearing capacity of liquid ball bearing, have the feature that, packet
Include following steps:
Step 1, the lubrication equation of hydrodynamic and hydrostatic pressure ball bearing, expression formula are established are as follows:
In formula:H indicates dimensionless oil film thickness；Indicate dimensionless oil film pressure；W is indicated
Revolving speed；η indicates coefficient of viscosity；PaIndicate atmospheric pressure；h0Indicate oil clearance；R indicates bearing radius；
Step 2, hydrodynamic lubrication oil film pressure computation model is established in the difference expression of spherical coordinate system:
Atmospheric boundary condition:
The liquid of certain pressure is injected by throttle orifice, static pressure boundary condition:
In formula: n is throttle orifice number, selects quantity for even number,
The pressure condition of continuity:
Each node pressure is modified using method of relaxation, method of relaxation expression formula are as follows:
In formula: ω is relaxation factor, general value 0~2；K is iteration coefficient.Indicate k+1 oil film pressure value,Indicate k oil film pressure value,Indicate k+1 dimensionless oil film pressure value；
Step 3, according to bearing parameter and boundary condition, the oil film thickness of bearing is calculated；
Step 4, initial pressure value is set, by the hydrodynamic lubrication oil film pressure computation model, calculates oil film pressure；
Step 5, by the oil film pressure in step 4, tri- Directional Decompositions of x, y and z are obtained under rectangular coordinate system
Px, PyAnd Pz,
Step 6, oil film circumferencial direction and radial direction pressure are integrated using Simpson's integration method, respectively obtains circumference x
The bearing capacity in direction, the circumferentially bearing capacity in the direction y and the radially bearing capacity in the direction z,
In formula: R indicates oil film radius,Indicate bearing radial direction initial angle,Indicate ball bearing Radial Integrals cornerite；
Step 7, it to formula (4) nondimensionalization, obtains
In formula: Wx, WyAnd WzRespectively indicate the dimensionless bearing capacity along tri- directions x, y and z；
Step 8, formula (5) is integrated using Simpson, obtains the bearing capacity of bearing are as follows:
Fx=pa·R2Wx (6)
The bearing capacity of other both directions is calculated, wherein radial bearing capacity expression formula is respectively as follows:
Above formula nondimensionalization is obtained:
In formula: W indicates dimensionless radial direction bearing capacity.
In the calculation method of the stable state bearing capacity of liquid ball bearing provided by the invention, there can also be such spy
Sign: where in step 3, according to bearing parameter and boundary condition, calculate the distribution of bearing film pressure.
The action and effect of invention
The bearing capacity of liquid ball bearing is the important indicator of bearing static characteristic, mainly by oil film pressure and shaft strength face
The influence of product size.The calculation method of the stable state bearing capacity of liquid ball bearing of the invention gives liquid spheres under spherical coordinate system
The calculation method of the stable state bearing capacity of bearing, after the pressure distribution including obtaining ball bearing, to liquid spheres loading ability of bearing energy
Power calculates；Oil film circumferencial direction and radial direction pressure are integrated using Simpson's integration method, respectively obtain holding for the direction circumference x
Loading capability, the circumferentially bearing capacity in the direction y and the radially bearing capacity in the direction z.
The stable state bearing capacity for the liquid ball bearing that calculation method of the invention can obtain is the result is that based on three-dimensional shafting.Cause
This, which can preferably reflect truth, preferably can provide theoretical direction for the structure design of liquid ball bearing.
The calculation method has filled up the notch of the stable state bearing capacity calculation of liquid ball bearing.
Detailed description of the invention
Fig. 1 is liquid ball bearing geometrical model schematic diagram in the embodiment of the present invention；
Fig. 2 is solution domain grid dividing schematic diagram in the embodiment of the present invention；
Fig. 3 is oil film thickness and pressure distribution schematic diagram in the embodiment of the present invention；And
Fig. 4 is rotor balancing position view in the embodiment of the present invention.
Specific embodiment
It is real below in order to be easy to understand the technical means, the creative features, the aims and the efficiencies achieved by the present invention
Example combination attached drawing is applied to be specifically addressed the calculation method of the stable state bearing capacity of liquid ball bearing of the invention.
Embodiment
Dynamic and static pressure liquid ball bearing exports the oil liquid of certain pressure by oil pump, flows into bearing clearance by flow controller and is formed
Static pressure oil film simultaneously forms static pressure bearing capacity, on the other hand, by running at high speed between bearing surface, between rotor and stator
Wedge shape oil is formed, dynamic pressure oil film is generated and forms dynamic pressure bearing capacity.By analyzing the oil film pressure in oil pocket, can calculate
The bearing capacity of oil film.
The object that the present embodiment is studied is liquid spheres bearing, initially sets up ball bearing threedimensional model.As shown in Figure 1, fixed
Throttle orifice 4 is provided in son 1, rotor 2 is arranged in stator 1, and main shaft 3 is arranged in rotor 2 and rotor 2 is driven to rotate, fuel feeding
System 5 passes through the fuel feeding into stator 1 of throttle orifice 4.Wherein: PaIndicate atmospheric pressure, d0Indicate that orifice diameter, R indicate convex ball half
Diameter, O indicate that the centre of sphere, r indicate the radius of recessed ball, PsIndicate aperture charge oil pressure,Indicate that fuel feeding cuts angle,Indicate cornerite,
h0Indicate average oil clearance, d1Indicate major axis diameter.
1, the steady of hydrodynamic and hydrostatic pressure ball bearing is established according to the liquid ball bearing geometrical model of Fig. 1 and hydrodynamic lubrication principle
State dimensionless hydrodynamic lubrication oil film pressure computation model:
In formula:H indicates dimensionless oil film thickness；Indicate dimensionless oil film pressure；W is indicated
Revolving speed；η indicates coefficient of viscosity；PaIndicate atmospheric pressure；h0Indicate oil clearance；R indicates bearing radius r,AndPoint
It Biao Shi not lower three coordinate directions of spherical coordinate system.
2, the oil film pressure computation model of ball bearing is two-dimensional partial differential equation, generallys use finite difference calculus and asks it
Solution, under generalized coordinates system in above formula pressure P and oil film thickness H respectively on staggered-mesh use centered Finite Difference Methods,
To its discretization, finite-difference expression under limit is derived, as shown in Fig. 2, obtaining greatly in conjunction with oil film pressure computation model
Gas boundary condition, the pressure condition of continuity and hydrostatic pressure condition acquire oil film pressure distribution.
Difference expression of the hydrodynamic lubrication oil film pressure computation model in spherical coordinate system are as follows:
Atmospheric boundary condition:
The liquid of certain pressure is injected by throttle orifice, static pressure boundary condition:
In formula: n is throttle orifice number, selects quantity for even number, generally selects 4,6 or 8.
The pressure condition of continuity:
Each node pressure is modified using method of relaxation, method of relaxation expression formula are as follows:
In formula: ω is relaxation factor, general value 0~2；K is iteration coefficient.Indicate k+1 oil film pressure value,Indicate k oil film pressure value,Indicate k+1 dimensionless oil film pressure value.
Bearing calculating parameter is as shown in table 1.
1 bearing parameter table of table
The oil film thickness (left side figure) and oil of bearing as shown in Figure 3 can be calculated according to bearing parameter and boundary condition
Film pressure (right side figure) distribution.
3, initial pressure value is set, obtains oil film pressure distribution, oil film pressure side by solving oil film pressure computation model
To always perpendicular to spherical surface, by oil film pressure, tri- Directional Decompositions of x, y and z obtain P under rectangular coordinate systemx, PyAnd Pz,
Specifically as shown in figure 4, the oil film pressure of all directions to be multiplied and be used pungent general with the cellar area of pressure effect respectively
Gloomy integration method integrates oil film circumferencial direction and radial direction pressure, the bearing capacity that respectively obtains the direction circumference x, circumferentially y
The bearing capacity in direction and the radially bearing capacity in the direction z.
In Fig. 4: exIndicate the eccentricity about the direction x, eyIndicate the eccentricity about the direction y, ezIt indicates about the direction z
Eccentricity, ω indicates that angular speed, t indicate the time, and θ indicates circumferential angle,Indicate meridian direction angle, Fx,FyAnd FzPoint
Oil film pressure Biao Shi not be indicated along the bearing capacity in tri- directions x, y and z, P.
Liquid oil film pressure direction is always perpendicular to bearing spherical surface tangential direction, by pressure along rectangular coordinate system x, y and z tri-
A Directional Decomposition is available:
In formula: R indicates oil film radius,Indicate bearing radial direction initial angle,Indicate ball bearing Radial Integrals cornerite.
Bearing capacity formula nondimensionalization, which will be calculated, can be obtained:
In formula: Wx, WyAnd WzRespectively indicate the dimensionless bearing capacity along tri- directions x, y and z.
Above formula is integrated using Simpson, numerical solution obtains the bearing capacity of bearing are as follows:
Fx=pa·R2Wx (6)
The bearing capacity of other both directions can be equally calculated, wherein radial bearing capacity expression formula is respectively as follows:
Above formula nondimensionalization is obtained:
In formula: W indicates dimensionless radial direction bearing capacity
In summary, it is first determined ball bearing parameter calculates each node oil film thickness, then passes through setting initial pressure
Value, calculates each node oil film pressure, constantly updates each node pressure value, finally calculate separately the carrying energy in tri- directions x, y and z
Power and axial carrying capacity and radial bearing capacity.
The action and effect of embodiment
The bearing capacity of liquid ball bearing is the important indicator of bearing static characteristic, mainly by oil film pressure and shaft strength face
The influence of product size.The calculation method of the stable state bearing capacity of the liquid ball bearing of the present embodiment gives liquid under spherical coordinate system
The calculation method of the stable state bearing capacity of ball bearing, after the pressure distribution including obtaining ball bearing, to liquid spheres loading ability of bearing
Capacity calculation；Oil film circumferencial direction and radial direction pressure are integrated using Simpson's integration method, respectively obtain the direction circumference x
Bearing capacity, the circumferentially bearing capacity in the direction y and the radially bearing capacity in the direction z.
The stable state bearing capacity for the liquid ball bearing that the calculation method of the present embodiment can obtain is the result is that based on three-dimensional shafting.
Therefore, which can preferably reflect truth, preferably can provide theory for the structure design of liquid ball bearing and refer to
It leads.
The calculation method has filled up the notch of the stable state bearing capacity calculation of liquid ball bearing.
Above embodiment is preferred case of the invention, the protection scope being not intended to limit the invention.
Claims (2)
1. a kind of calculation method of the stable state bearing capacity of liquid ball bearing, which comprises the following steps:
Step 1, the lubrication equation of hydrodynamic and hydrostatic pressure ball bearing, expression formula are established are as follows:
In formula:H indicates dimensionless oil film thickness；Indicate dimensionless oil film pressure；W indicates revolving speed；η
Indicate coefficient of viscosity；PaIndicate atmospheric pressure；h0Indicate oil clearance；R indicates bearing radius；
Step 2, hydrodynamic lubrication oil film pressure computation model is established in the difference expression of spherical coordinate system:
Atmospheric boundary condition:
The liquid of certain pressure is injected by throttle orifice, static pressure boundary condition:
In formula: n is throttle orifice number, selects quantity for even number,
The pressure condition of continuity:
Each node pressure is modified using method of relaxation, method of relaxation expression formula are as follows:
In formula: ω is relaxation factor, general value 0~2；K is iteration coefficient.Indicate k+1 oil film pressure value,Table
Show k oil film pressure value,Indicate k+1 dimensionless oil film pressure value；
Step 3, according to bearing parameter and boundary condition, the oil film thickness of bearing is calculated；
Step 4, initial pressure value is set, by the hydrodynamic lubrication oil film pressure computation model, calculates oil film pressure；
Step 5, by the oil film pressure in step 4, tri- Directional Decompositions of x, y and z obtain P under rectangular coordinate systemx, PyWith
And Pz,
Step 6, oil film circumferencial direction and radial direction pressure are integrated using Simpson's integration method, respectively obtains the direction circumference x
Bearing capacity, the circumferentially bearing capacity in the direction y and the radially bearing capacity in the direction z,
In formula: R indicates oil film radius,Indicate bearing radial direction initial angle,Indicate ball bearing Radial Integrals cornerite；
Step 7, it to formula (4) nondimensionalization, obtains
In formula: Wx, WyAnd WzRespectively indicate the dimensionless bearing capacity along tri- directions x, y and z；
Step 8, formula (5) is integrated using Simpson, obtains the bearing capacity of bearing are as follows:
Fx=pa·R2Wx (6)
The bearing capacity of other both directions is calculated, wherein radial bearing capacity expression formula is respectively as follows:
Above formula nondimensionalization is obtained:
In formula: W indicates dimensionless radial direction bearing capacity.
2. the calculation method of the stable state bearing capacity of liquid ball bearing according to claim 1, it is characterised in that:
Wherein, in step 3, according to bearing parameter and boundary condition, the distribution of bearing film pressure is calculated.
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| CN111207922A (en) * | 2020-01-14 | 2020-05-29 | 中国北方车辆研究所 | High-power high-rotation-speed planetary speed change mechanism test device |
| CN112069710A (en) * | 2020-09-07 | 2020-12-11 | 电子科技大学 | Prediction method for self-excited vibration of gas static pressure main shaft |
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